In conventional floating point arithmetic systems, numbers are represented with an exponent and a fraction which is called the mantissa. The mantissa is always between the radix and one over the radix. For example, if the radix is 10, the mantissa would be between 0.1 and 1.0. If the radix is 2, the mantissa would be between 0.5 and 1.0. When addition or subtraction is performed, the exponents are first compared. If they are the same, then the addition or subtraction can proceed immediately. If they are different, the mantissa of the number with the smaller exponent must be down-shifted (shifted to the right) and one or more leading zeros inserted until the two exponents are the same. Then addition can proceed. Subtraction is often done by complementing the subtrahend and then performing addition. Conventional floating point systems utilize a four-step procedure. The first step is to align the two mantissas, that is, compare the magnitude of the exponents and then shift the smaller mantissa to the right the number of places required to make the exponent of the smaller number equal to the exponent of the larger number. In the second step, the two numbers, the addend and the augend, are added together to get the sum or, in subtraction, the subtrahend is subtracted from the minuend to obtain the difference. The mantissa which is a subtrahend or augend is generally accompanied by three additional digits, the guard digit, the round digit and the sticky digit which are used for purposes of rounding when the mantissa is shifted. In some techniques, subtraction is accomplished by complementing the subtrahend and then adding the subtrahend and minuend. The third step is normalization. If, during addition, the mantissa overflows it will be shifted to the right and the exponent will be raised 1 power. If there is no overflow, no shifting is required. In subtraction, if the difference has one or more leading zeroes then the mantissa must be shifted to the left and the exponent decremented by the number of leading zeroes. In either the overflowed addition operation or the subtraction operation that ended with leading zeroes, a decision has then to be made. In the fourth step, the normalized result is rounded. In the addition overflow situation, the least significant digit is rounded. If there is no overflow, the guard digit is rounded. In a subtraction operation where there results a leading zero in the difference, the round digit is rounded and, when there is no leading zero, the guard digit is rounded. This approach requires a second addition operation which may result in a second normalization.